Jourdain’s variational equation and Appell’s equation of motion for nonholonomic dynamical systems

Abstract

Based on Jourdain’s variational equation proposed in 1909, we deduce a minimal set of general equations of motion for nonholomic dynamical systems of particles and rigid bodies. This equation of motion for the system, which differs slightly from the Gibbs–Appell equation, appears to be the same as the equation derived by Kane in 1961. Since the same equation was established by Appell in 1903 on the basis of D’Alembert’s principle, the newly derived equation is named Appell’s equation.